# std::exponential_distribution

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< cpp‎ | numeric‎ | random

Defined in header `<random>` |  |
template< class RealType = double > class exponential_distribution; |  | (since C++11)

Produces random non-negative floating-point values \(\small x\)x, distributed according to probability density function:

  \(\small P(x|\lambda) = \lambda e^{-\lambda x}\)P(x|λ) = λe-λx

The value obtained is the time/distance until the next random event if random events occur at constant rate \(\small\lambda\)λ per unit of time/distance. For example, this distribution describes the time between the clicks of a Geiger counter or the distance between point mutations in a DNA strand.

This is the continuous counterpart of std::geometric_distribution.

`std::exponential_distribution` satisfies RandomNumberDistribution.

### Template parameters

RealType | - | The result type generated by the generator. The effect is undefined if this is not one of float, double, or long double.

### Member types

Member type | Definition
`result_type` (C++11) | RealType
`param_type` (C++11) | the type of the parameter set, see RandomNumberDistribution.

### Member functions

(constructor) (C++11) | constructs new distribution (public member function)
reset (C++11) | resets the internal state of the distribution (public member function)
##### Generation
operator() (C++11) | generates the next random number in the distribution (public member function)
##### Characteristics
lambda (C++11) | returns the lambda distribution parameter (rate of events) (public member function)
param (C++11) | gets or sets the distribution parameter object (public member function)
min (C++11) | returns the minimum potentially generated value (public member function)
max (C++11) | returns the maximum potentially generated value (public member function)

### Non-member functions

operator==operator!= (C++11)(C++11)(removed in C++20) | compares two distribution objects (function)
operator<<operator>> (C++11) | performs stream input and output on pseudo-random number distribution (function template)

### Notes

Some implementations may occasionally return infinity if `RealType` is float. This is LWG issue 2524.

### Example

Run this code

    #include <iomanip>
    #include <iostream>
    #include <map>
    #include <random>
    #include <string>

    int main()
    {
        std::random_device rd;
        std::mt19937 gen(rd());

        // if particles decay once per second on average,
        // how much time, in seconds, until the next one?
        std::exponential_distribution<> d(1);

        std::map<int, int> hist;
        for (int n = 0; n != 10000; ++n)
            ++hist[2 * d(gen)];

        for (auto const& [x, y] : hist)
            std::cout << std::fixed << std::setprecision(1)
                      << x / 2.0 << '-' << (x + 1) / 2.0 << ' '
                      << std::string(y / 200, '*') << '\n';
    }

Possible output:

    0.0-0.5 *******************
    0.5-1.0 ***********
    1.0-1.5 *******
    1.5-2.0 ****
    2.0-2.5 **
    2.5-3.0 *
    3.0-3.5
    3.5-4.0

### External links

Weisstein, Eric W. "Exponential Distribution." From MathWorld — A Wolfram Web Resource.

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